Research On Rank Deficiency In Image Reconstruction Of Oil-gas Lubrication ECT System

Electrical capacitance tomography(ECT)plays an important role in the real-time detection of oil-gas two-phase flow parameters in a closed oil-gas lubrication pipeline.A typical discrete ill posed problem appears in the process of image reconstruction,and then the serious effect on the quality of image reconstruction will be produced due to the rank deficiency problem,ill posed problem and ECT’s inherent "soft field" effect attribute.Therefore,the rank defect problem of oil-gas lubrication ECT system is studied deeply in this thesis in view of its characteristics,such as small pipe diameter,thin oil film and finite number of plates,and the main research work and conclusions are as follows,(1)The mathematical model and simulation model of sensitivity matrix,deduced from the oil-gas lubrication ECT system,are established,the main causes of rank deficiency and its influencing factors are analyzed,and the two evaluation indexes,the rank deficiency number and relative rank deficiency rate,are defined in order to analyze the rank deficiency problem.The results show that there is serious rank deficiency in the sensitivity matrix of the system.The produce of rank deficiency of sensitivity matrix is related to the structure and application of oil-gas lubrication ECT system,and the root cause of rank deficiency is the lack of analyzing data from sensors in image reconstruction.(2)It is confirmed that there is serious soft field effect in the oil-gas lubrication system with small pipe diameter after the sensitive field analysis of the sensor area is done,and then the measurement method of the soft field effect is proposed.The producing causes and influencing factors of the rank deficiency problem in image reconstruction,taking over the soft field effect or not,are analyzed and compared employing the rank deficiency number and relative rank deficiency rate defined above.The results show that there is still a serious rank deficiency problem in the ECT system taking over the soft field effect,while the rank deficiency of the sensitivity matrix is reduced compared with the system without taking over the soft field effect.(3)The rank deficiency problem existing in LBP algorithm,Tikhonov regularization algorithm,conjugate gradient algorithm and biconjugate gradient algorithm are analyzed based on the principle of image reconstruction algorithm.The physical model and simulation model of ECT system with annular flow are established,and then LBP algorithm,Tikhonov algorithm,conjugate gradient algorithm and biconjugate gradient algorithm are respectively employed to reconstruct the image of oil-gas lubrication ECT system,and the image reconstruction results are analyzed and compared finally using evaluation indexes IME and CORR.The results show that except LBP algorithm,the rest algorithms reflect the idea of eliminating rank deficiency in the process of the image reconstruction.The biconjugate gradient algorithm,which can completely eliminate the rank deficiency of sensitivity matrix,has higher imaging accuracy and faster imaging speed than other algorithms and is more suitable for real-time imaging of oil-gas lubrication ECT system.